Question

Find the approximate value of (82)^1/4.

(a) 3.025

(b) 3.05

(c) 3.00925

(d) 3.07825

This question was posed to me in exam.

This key question is from Derivatives Application topic in section Application of Derivatives of Mathematics – Class 12

Answer 1

Right answer is (c) 3.00925

Easiest explanation: Let y=x^1/4. Let x=81 and Δx=1

Then, Δy=(x+Δx)^1/4-x^1/4

 Δy=82^1/4-81^1/4

82^1/4=Δy+3

dy is approximately equal to Δy is equal to

dy=\(\frac{dy}{dx}\)Δx

dy=\(\frac{1}{(4x^{3/4})}\).Δx

dy=\(\frac{1}{(4×81^{3/4})} (1)\)

dy=\(\frac{1}{(4×27)}\)=0.00925

∴ The approximate value of 82^1/4 is 3+0.00925=3.00925